A method of milking an animal by means of a milking device (1) provided with at least one teat cup (2) having a pulsation space and a teat space. The teat space is connected to a vacuum source via (10) a milk tube (5a,5b), the teat space and the milk tube forming a milking space, which method comprises successively a connection step, a milk-drawing step and a disconnection step. During the milk-drawing step a pulsating pulsation vacuum is present in the pulsation space and a milking vacuum is present in the teat space. In the disconnection step the milking vacuum is lowered after which the teat cup is drawn away from the animal by the device, the vacuum level being measured in a part of the milking space. The teat cup is drawn away after the vacuum level has come below a threshold value. A milking device (1) provided with a robot (14) for automatically connecting at least one teat cup (2) to a teat of an animal, which teat cup (2) comprises a teat space for containing a teat and a pulsation space for applying a milking motion by means of a pulsating pulsation vacuum. The teat space is connected via a milk tube (5a,5b) to a vacuum source (10) for generating a milking vacuum. The teat space and the milk tube form the milking space, with a drawing-away device (3) for drawing the teat cup (2) away from the animal, with a vacuum-lowering device for lowering the milking vacuum in the teat space, with a computer (11) for activating the drawing-away device (3) after the milking vacuum has been lowered, the milking space comprising a sensor (16) for measuring the milking vacuum and emitting to the computer (11) a milking vacuum signal. The drawing-away device (3) is capable of being activated when the vacuum level comes below a threshold value.
